CoCalc
Sharedsupport / 2015-05-03-173407-elliptic-curve.sagewsOpen in CoCalc

Examples for support purposes...

Points on y2=x(x3)(x+4)y^2 = x(x-3)(x+4).

expand(x*(x-3)*(x+4))
x^3 + x^2 - 12*x
E = EllipticCurve([0,1,0,-12,0]); show(E)
y2=x3+x212x\displaystyle y^2 = x^{3} + x^{2} - 12 x
E.conductor()
168
E.rank()
0
E.cremona_label()
'168a2'
E.integral_points()
[(-4 : 0 : 1), (0 : 0 : 1), (3 : 0 : 1)]
E.torsion_points()
[(-4 : 0 : 1), (0 : 0 : 1), (0 : 1 : 0), (3 : 0 : 1)]